where \(l=0,\,1,\,2\,\ldots \)  is the orbital quantum number and \(E\)  the energy of the scalar field.
It is easily seen that Eq. (REF ) portrays the radial equation of motion for a scalar field in the Schwarzschild BH background. At this point we need to modify the squared low-energy 3-momentum, i.e., \(p_{0}^{2}\) , due to the GUP and for this reason we utilize Eq. (REF )The angular part can be GUP modified as well [1]}, although since it does not contain any black hole parameters, it is insensitive to them. Therefore, the result, i.e., discreteness of space in those directions, would not differ from those found in flat spacetimes as well as in weak gravitational backgrounds [2]}, [3]}, [4]}, [5]}.. Therefore, the squared low-energy 3-momentum, i.e., \(p_{0}^{2}\) , will be transformed to the high-energy 3-momentum, i.e., \(p_{i}^{2}\) , as follows [2]}, [4]}
\(p_{0}^{2}\rightarrow \,p_{i}^{2}=-\hbar ^2\, \nabla ^2\,\psi (r)-2\,i\alpha \hbar ^3\, \nabla ^2(\nabla \psi (r))+5\alpha ^2\hbar ^4 \, \nabla ^2(\nabla ^2 \psi (r))\) 
